What is an XYZ-Wing?
An XYZ-Wing is a pivot cell with exactly three candidates XYZ, plus two cells it sees with two candidates each: XZ and YZ. If the pivot is X, the XZ wing is Z. If it is Y, the YZ wing is Z. If it is Z, the pivot itself is Z. So one of the three cells is Z, and any cell that sees all three loses Z.
Because the victim must see the pivot too, it usually sits in the pivot’s box and in a row or column with one wing. That makes XYZ-Wings easy to check once you know where to look. In Marble Sudoku you look for a hole with three small marbles next to holes with two.
Use one in 3 moves
- 1Pivot. Find a cell with exactly three candidates, X, Y and Z.
- 2Wings. Find two two-candidate cells it sees: one XZ, one YZ.
- 3Clear. Remove Z from every cell that sees the pivot and both wings.
Then look for singles where Z was removed.
TRY IT · GUIDED EXAMPLE
Build the XYZ-Wing
Small marbles show the colors left in every hole with two or three. Tap the pivot, find its two wings, watch why Sky must be in one of the three, and clear Sky where all three can see.
This is the real board from Marble Sudoku. The nine marble colors stand for the numbers 1 to 9.
- Pivot
- Wings
- Clear
- Place
Build the XYZ-Wing
Read the example in words
Row 1, column 5 can be Pink, Yellow or Sky: that is the pivot. In the same row, row 1, column 1 is Pink or Sky. In the same box, row 2, column 5 is Yellow or Sky. If the pivot is Pink, the first wing is Sky. If it is Yellow, the second wing is Sky. If it is Sky, the pivot is Sky. Row 1, column 4 sees all three (the same row as the pivot and the first wing, the same box as the second), so it can’t be Sky, and only Orange is left. With numbers turned on, Pink is 3, Yellow is 6, Sky is 9 and Orange is 1.
YOUR TURN · PRACTICE
Spot the XYZ-Wings
Each round shows the small marbles in every hole with two or three colors. Tap a three-color pivot and its two wings. On Easy the pivot is ringed. On Hard you find all three yourself.
Round color:
Why an XYZ-Wing works
The pivot can only be X, Y or Z. If it is X, the XZ wing sees it and can’t be X, so it is Z. If it is Y, the YZ wing must be Z. If it is Z, the pivot is Z. In all three cases, one of the three cells holds Z.
A cell that sees the pivot and both wings would clash with whichever of them is Z. So it can’t be Z. A cell that sees only the two wings is not enough here, because the Z might be in the pivot.
How to spot XYZ-Wings faster
- Start from three-candidate cells. Every XYZ-Wing has a pivot with exactly three candidates. Check those cells one by one.
- Wings are subsets. Each wing has two of the pivot’s three numbers, and both wings share the same one, Z.
- Look in the pivot’s box. One wing is usually in the pivot’s box and the other in its row or column. The victims sit where those overlap.
- Expect few eliminations. Only cells that see all three can lose Z, so there are rarely more than two. One is often enough.
XYZ-Wing vs. Y-Wing vs. Naked Triple
| XYZ-Wing | Y-Wing | Naked Triple | |
|---|---|---|---|
| Pivot | Three candidates: XYZ | Two candidates: XY | No pivot: three cells in one unit |
| Wings | XZ and YZ | XZ and YZ | — |
| Victims must see | The pivot and both wings | Both wings | Any cell in the same unit |
| Difficulty | Advanced | Advanced | Intermediate |
Common mistakes
- Clearing cells that see only the wings. That works for a Y-Wing, not here. The pivot can be Z too, so a victim must see the pivot as well.
- Wings with a number outside the pivot. Both numbers of each wing must be in the pivot. XW is not a wing for an XYZ pivot.
- Two identical wings. The wings must be XZ and YZ. Two XZ wings don’t cover the case where the pivot is Y.
- Pivot with four candidates. The pivot needs exactly three. With four, there is a case where none of the cells is Z.
XYZ-Wing FAQ
What is an XYZ-Wing in Sudoku?
An XYZ-Wing is a pivot cell with three candidates XYZ and two wing cells it sees, XZ and YZ. One of the three cells must be Z, so Z can be removed from every cell that sees all three.
How is it different from a Y-Wing?
In a Y-Wing the pivot has only X and Y, so the Z is in one of the wings and victims only need to see both wings. In an XYZ-Wing the pivot also has Z, so victims must see the pivot too.
Where do the eliminations usually happen?
In the pivot’s box, on the row or column it shares with one wing. Those are the only cells that can see all three.
Do the wings have to see each other?
No. Each wing must see the pivot. The wings don’t need to see each other.
Does this work in Marble Sudoku?
Yes. Find a hole with exactly three colors left and two holes it sees with two of those colors each, sharing one color. Remove that shared color from every hole that sees all three.
When should I look for one?
After Y-Wings. If a hard puzzle has three-color holes with two-color neighbors, an XYZ-Wing is worth a check.
PRACTICE IN THE GAME
Find XYZ-Wings in a real puzzle
When a hard puzzle stalls, look for a hole with three colors left next to holes with two. If the wings match, the shared color can go from the box.
Next techniqueUnique Rectangle
